# What is Elasticity, Elastic Limit, Young’s Modulus and Modulus of Rigidity in Strength of Materials?

In this article we will learn about what is elasticity, elastic limit, young’s modulus and modulus of rigidity. These terms keeps an important role in the study of subject strength of materials. Understanding about stress and strain is possible when one must have the knowledge of these terms. Let’s discuss about them one by one.

### What is Elasticity?

When an external force is applied on a body and it undergoes

some deformation. If the body returns back to its original shape and size on

complete removal of the load, the body is called elastic body. This property by

which any material regains its original shape and size when load acting on it

is completely removed is called elasticity.

some deformation. If the body returns back to its original shape and size on

complete removal of the load, the body is called elastic body. This property by

which any material regains its original shape and size when load acting on it

is completely removed is called elasticity.

**Elasticity:**The property of a material by which it returns

back to its original position (i.e. shape and size) on the removal of external force or load,

is called elasticity.

### What is Elastic Limit?

A body will return back to its original shape and size when

the deformation caused by the external force, is within certain limit. There is

a limiting value of force upto and within which the deformation caused completely

disappears on the removal of external force. The value of stress corresponding

to this limiting force is known as elastic limit of the material.

the deformation caused by the external force, is within certain limit. There is

a limiting value of force upto and within which the deformation caused completely

disappears on the removal of external force. The value of stress corresponding

to this limiting force is known as elastic limit of the material.

**Elastic Limit:**It is defined as the value of stress upto and

within which the material return back to their original position (i.e. shape

and size) on the removal of external force.

If the value of external force is such that it exceeds the

elastic limit, than the body will not completely regain its original position. The

body loses its property of elasticity to some extent. And if the external force

acting on the body is removed, in that condition the body will not return to

its original shape and size and there will be a residual deformation in the

material.

elastic limit, than the body will not completely regain its original position. The

body loses its property of elasticity to some extent. And if the external force

acting on the body is removed, in that condition the body will not return to

its original shape and size and there will be a residual deformation in the

material.

### What is Young’s Modulus?

**Young’s Modulus:**The ratio of tensile or compressive stress

to the corresponding strain within elastic limit is called young’s modulus.

- Young’s modulus is also known as modulus of elasticity. It is

denoted by E. - The formula of Young’s modulus is given by

Where

σ = Tensile or compressive stress,

e = Tensile or compressive strain,

E = young’s modulus or modulus of elasticity.

### What is Modulus of Rigidity?

**Modulus of Rigidity or Shear Modulus:**It is defined as the ratio

of shear stress to the corresponding

shear strain within elastic limit.

- It is denoted by C or G or N
- The formula of modulus of rigidity is given by

Where

τ = Shear stress

ɸ = Shear stress

C = Modulus of rigidity

This is all about what is elasticity, elastic limit, young’s modulus and modulus of rigidity. If you find anything missing or incorrect than comment us. And if you like this article than like us on Facebook.

Moduli of elasticity are defined within the limit of proportionality